To have the parents appear separately under the Student in the Student Parent Directory (Verdana) report, you would need to remove the Spouse relationship from the parents.

As a Platform Manager:
  1. Navigate to Core.
  2. Select People Finder.
  3. Search/select one of your parents.
  4. On their Contact Card tab, scroll down to Relationships. 
  5. Click Manage.
  6. Check the Remove box to the right of the user with the Spouse/Partner relationship.
  7. Save.
This will then allow the parents to appear separately on the Student Parent Directory (Verdana) report.